Application of Monte Carlo techniques to grain boundary structure optimization in silicon and silicon-carbide
M Guziewski and AD Banadaki and S Patala and SP Coleman, COMPUTATIONAL MATERIALS SCIENCE, 182, 109771 (2020).
While classical atomistic simulations are commonly used to study energetically favorable structures of grain boundaries, the determination of these structures oftentimes comes at a significant computational cost for each grain boundary surveyed. This arises from the need to sample many microscopic degrees of freedom within the grain boundary even when the five macroscopic degrees of freedom are known. Recent work has proposed the use of a Monte Carlo approach to grain boundary optimization, in which atoms are iteratively added or removed from the grain boundary region and the resultant structure accepted or rejected according to the Metropolis criterion. This enables the rapid sampling of microscopic degrees of freedom, thus decreasing the computational costs required to find minimum energy structures. However thus far, this approach has only been applied to single element, metallic systems of the bcc and fcc structure. This work expands the Monte Carlo grain boundary optimization approach to ceramic systems, considering the more complex diamond cubic (Silicon) and zinc blende (multi-element Silicon Carbide) crystal structures. The novel contributions of this article involve modifications to the Monte Carlo approach necessary for systems with multiple elements and covalent bonding, which results a complex energy landscape with significantly more local minima. The Monte Carlo algorithm is applied to a variety of symmetric tilt and twist grain boundaries, and the determined minimum energy structures are found to be in good agreement with literature. The algorithm also samples over a range of non-equilibrium grain boundary structures, allowing for a quantification of the metastability of grain boundaries. These results raise the possibility of expanding the Monte Carlo approach to other material systems and its use as a robust tool in better characterizing grain boundaries and other interfaces.
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